Thinking Cap 4 by Pelangi Publishing

Mathematics Primary 4 Unit 1 Whole Numbers (1)

Whole Numbers (1)

otes Rounding off Numbers to the Nearest Ten When we round a number to the nearest ten we must decide whether to take it to the ten before the number or the after the number.

The halfway point between two tens always ends in 5. Any number from 5 to the next ten is rounded up to the next ten. Any number less than 5 is rounded to the ten before.

Round to

The nearest tens are 10 and 20.

110

113

120

113 is between 110 and 120. It is nearer to 110 than to 120. 113 is 110 when rounded off to the nearest ten. 113  110

It shows that 113 is before the halfway point. We should round it to the nearest ten before which is 10.

Round to

The nearest tens are 10 and 20.

110

120

118 is between 110 and 120. It is nearer to 120 than to 110. 118 is 120 when rounded off to the nearest ten. 118  120

It shows that 118 is after the halfway point. We should round it to the nearest ten after which is 20.

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118

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Mathematics Primary 4 Unit 1 Whole Numbers (1)

Round to

The nearest tens are 10 and 20.

110

115

120

115 is exactly halfway between 110 and 120. 115 is 120 when rounded off to the nearest ten. 115  120

It shows that 115 is exactly on halfway point. We should round it to the nearest ten after which is 20.

Rounding off Numbers to the Nearest Hundred

The halfway point between two hundreds always ends in 50. We must decide whether the number we are rounding is greater than or less than the halfway point.

If the number is less than the halfway point, we round it to the hundred before. If it is on the halfway point or greater than it, we round it to the next hundred.

Round to

The nearest hundreds are 100 and 200.

1125

1200

1125 is between 1100 and 1200. It is nearer to 1100 than to 1200. 1125 is 1100 when rounded off to the nearest hundred. 1125  1100

It shows that 1125 is before the halfway point. We should round it to the nearest hundred before which is 100.

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1100

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Mathematics Primary 4 Unit 1 Whole Numbers (1)

Round to

The nearest hundreds are 100 and 200.

1100

1180

1200

1180 is between 1100 and 1200. It is nearer to 1200 than to 1100. 1180 is 1200 when rounded off to the nearest hundred. 1180  1200

It shows that 1180 is after the halfway point. We should round it to the nearest hundred after which is 200.

Round to

The nearest hundreds are 100 and 200.

1100

1200

1150 is exactly halfway between 1100 and 1200. 1150 is 1200 when rounded off to the nearest hundred. 1150  1200

It shows that 1150 is exactly on the halfway point. We should round it to the nearest hundred after which is 200.

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1150

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Mathematics Primary 4 Unit 1 Whole Numbers (1)

xample 1 Denise cut a ribbon into three parts. The first part of the ribbon was 108 cm, the second part of the ribbon was 84 cm longer than the first part while the third part of the ribbon was twice as long as the second part. What was the length of the ribbon that Denise had at first? Round off your answer to the nearest ten centimetres.

olution First part

108 cm

84 cm

Second part Third part

? ?

108 cm + 84 cm = 192 cm The second part of the ribbon was 192 cm. 2 x 192 cm = 384 cm The third part of the ribbon was 384 cm. 108 cm + 192 cm + 384 cm = 684 cm The length of the ribbon that Denise had at first was 684 cm. Round to

680

684

685

690

684 is between 680 and 690. It is nearer to 680 than to 690. Therefore, 684 is 680 when rounded off to the nearest ten. 684  680 The length of the ribbon that Denise had at first was 680 cm when rounded off to the nearest ten centimetres. © Pelangi Publishing Singapore Pte. Ltd.

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Mathematics Primary 4 Unit 1 Whole Numbers (1)

xample 2 Angie, Brian and Cindy collected $830 in a fund raising activity. Angie collected $130 more than Brian. Cindy collected half the amount that Brian collected. How much money did Brian collect? Round off your answer to the nearest hundred dollars.

olution Angie $130

Brian

$830

? Cindy

5 units + $130 = $830 5 units = $830 – $130 = $700

1 unit = $700 ÷ 5 = $140

2 x $140 = $280

Brian collected $280. Round to

200

250

280

300

280 is between 200 and 300. It is nearer to 300 than to 200. Therefore, 280 is 300 when rounded off to the nearest hundred. 280  300 Brian collected $300 when rounded off to the nearest hundred dollars. 5

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Mathematics Primary 4 Unit 1 Whole Numbers (1)

xample 3 754

623

218

Round off each number to the nearest hundred. Then, estimate the value of: (a) 754 + 623 (b) 623 – 218

olution 7 5 4 700 800

6 2 3 600 700

2 1 8 200 300

754 is between 700 and 800. It is nearer to 800 than to 700. So, 754 is 800 when rounded off to the nearest hundred. 754  800 623 is between 600 and 700. It is nearer to 600 than to 700. So, 623 is 600 when rounded off to the nearest hundred. 623  600 218 is between 200 and 300. It is nearer to 200 than to 300. So, 218 is 200 when rounded off to the nearest hundred. 218  200

(a)

The value of 754 + 623 is about

(b)

754 + 623  800 + 600 = 1400

623 – 218  600 – 200 = 400

The value of 623 – 218 is about

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1400 .

400 .

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Mathematics Primary 4 Unit 1 Whole Numbers (1)

xample 4 Estimate the value of: (a) 489 × 3 (b) 632 ÷ 5

olution (a)

400

489

500

489 is 500 when rounded off to the nearest hundred. 489  500

So, 500 × 3 = 1500 The value of 489 × 3 is about

(b)

600

1500 .

632

700

632 is 600 when rounded off to the nearest hundred. 632  600

So, 600 ÷ 5 = 120 The value of 632 ÷ 5 is about

120 .

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Mathematics Primary 4 Unit 1 Whole Numbers (1)

ractice Solve the following word problems. 1. In a game, Matthew scored 123 points. Rachel scored 11 times as many points as Matthew. What was their total score in the game? Round off your answer to the nearest ten.

2. Round off 2268 ÷ 7 to the nearest hundred.

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Mathematics Primary 4 Unit 1 Whole Numbers (1)

3. The total height of Adam, Bobby and Clare is 444 cm. Bobby’s height is twice as much as Adam while Clare is 52 cm taller than Adam. What is the height of Adam. Round off your answer to the nearest ten centimetres.

4. Michelle prepared two types of ribbons for her art project in school. There were a total of 3 yellow ribbons and 5 green ribbons. The total length of the ribbons was 28 cm. If the length of each yellow ribbon is thrice the length of each green ribbon, find the total length of the 3 yellow ribbons.

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Mathematics Primary 4 Unit 1 Whole Numbers (1)

5. After purchasing a storybook and a lego set, Daniel had $12 left. The lego set cost 4 times as much as the storybook. If the lego set costs $48 more than the storybook, how much money did Daniel have at first? Round off your answer to the nearest ten dollars.

6. Linda and Janet went shopping with the same amount of money. Janet spent $65. Linda spent $14 and had twice as much money left as Janet. If both of them had $153 left altogether, how much money did Linda have at first? Round off your answer to the nearest ten dollars.

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Mathematics Primary 4 Unit 1 Whole Numbers (1)

7. Mr Johnson had four times as many fiction books as non-fiction books in his bookstore. At the end of the month, 250 of non-fiction books were sold. The number of the remaining fiction books became 8 times the number of the remaining non-fiction books. How many books were there in Mr Johnson’s bookstore at the end of the month? Round off your answer to the nearest hundred.

8. During Chinese New Year, Joan received 4 times as much red packet money as Josh. Joan spent $528 of her money and saved the rest. Josh saved up all the money and his money became thrice of Joan’s. How much money does Josh have now? Round off your answer to the nearest hundred dollars.

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Mathematics Primary 4 Unit 1 Whole Numbers (1)

9. Susan and Betty had a total of 414 badges in their collections. Susan gave 184 of her badges to Betty. Betty’s collection of badges became 5 times as many as Susan’s. How many badges did Betty have at first? Round off your answer to the nearest ten.

10. Anjeline has twice as many beads as Donna. Donna has 48 more beads than Esther. If the three of them have 648 beads altogether, how many more beads does Anjeline have than Esther?

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Mathematics Primary 4 Unit 1 Whole Numbers (1)

11. There were two types of fish in a pond. The number of angelfish was thrice as many as clownfish. 75 clownfish were moved to an aquarium. The number of angelfish in the pond became 6 times the number of the remaining clownfish. How many more angelfish than clownfish are there in the pond now?

12. The volume of water in Container A is 12 times the volume of water in Container B. Container B contains 238 ml of water. It contains 1095 ml of water less than Container C. Find the difference in volume of water between Container A and Container C. Round off your answer to the nearest ten millilitres.

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Mathematics Primary 4 Unit 2 Whole Numbers (2)

Whole Numbers (2)

otes Factors Product 12 12 12

Factors 1 × 12 2×6 3×4

12 can be divided exactly by 1, 2, 3, 4, 6 and 12.

Product

18 18 18

Factors 1 × 18 2×9 3×6

18 can be divided exactly by 1, 2, 3, 6, 9 and 18.

A number can be divided exactly by its factors without remainders.

Therefore, The factors of 12 are 1 , 2 , 3 , 4, 6 and 12. The factors of 18 are 1 , 2 , 3 , 6 , 9 and 18. The common factors of 12 and 18 are 1, 2, 3 and 6.

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Mathematics Primary 4 Unit 2 Whole Numbers (2)

Multiples First 12 multiples of 4: 1×4=4 5 × 4 = 20 9 × 4 = 36

2×4=8 6 × 4 = 24 10 × 4 = 40

3 × 4 = 12 7 × 4 = 28 11 × 4 = 44

4 × 4 = 16 8 × 4 = 32 12 × 4 = 48

These numbers can be divided exactly by 4. 4 is a factor of these numbers. First 12 multiples of 6: 1×6=6 5 × 6 = 30 9 × 6 = 54

2 × 6 = 12 6 × 6 = 36 10 × 6 = 60

3 × 6 = 18 7 × 6 = 42 11 × 6 = 66

4 × 6 = 24 8 × 6 = 48 12 × 6 = 72

These numbers can be divided exactly by 6. 6 is a factor of these numbers. Multiples of 4: 4, 8, 12 , 16, 20, 24 , 28, 32, 36 , 40, 44, 48 Multiples of 6: 6, 12 , 18, 24 , 30, 36 , 42, 48 , 54, 60, 66, 72 The common multiples of 4 and 6 are 12, 24, 36 and 48.

xample 1 Mrs Patterson has 35 scones to distribute equally among her pupils. What are the possible numbers of pupils Mrs Patterson has? (Assume there are more than 1 pupil.)

olution 35 = 1 × 35 35 = 5 × 7 The factors of 35 are 1, 5, 7 and 35. The possible numbers of pupils Mrs Patterson has are 5 , 7 and 35 . 15

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